Neural Optimal Transport Meets Multivariate Conformal Prediction

• URL: http://arxiv.org/abs/2509.25444v1
• Date: Mon, 29 Sep 2025 19:50:19 GMT
• Title: Neural Optimal Transport Meets Multivariate Conformal Prediction
• Authors: Vladimir Kondratyev, Alexander Fishkov, Nikita Kotelevskii, Mahmoud Hegazy, Remi Flamary, Maxim Panov, Eric Moulines,
• Abstract summary: We propose a framework for conditional vectorile regression (CVQR)<n>CVQR combines neural optimal transport with quantized optimization, and apply it to predictions.
• Score: 58.43397908730771
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a framework for conditional vector quantile regression (CVQR) that combines neural optimal transport with amortized optimization, and apply it to multivariate conformal prediction. Classical quantile regression does not extend naturally to multivariate responses, while existing approaches often ignore the geometry of joint distributions. Our method parametrizes the conditional vector quantile function as the gradient of a convex potential implemented by an input-convex neural network, ensuring monotonicity and uniform ranks. To reduce the cost of solving high-dimensional variational problems, we introduced amortized optimization of the dual potentials, yielding efficient training and faster inference. We then exploit the induced multivariate ranks for conformal prediction, constructing distribution-free predictive regions with finite-sample validity. Unlike coordinatewise methods, our approach adapts to the geometry of the conditional distribution, producing tighter and more informative regions. Experiments on benchmark datasets show improved coverage-efficiency trade-offs compared to baselines, highlighting the benefits of integrating neural optimal transport with conformal prediction.

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